rmevspec  R Documentation 
Generate from Q_i
, the spectral measure of a given multivariate extreme value model based on the L1 norm.
rmevspec(
n,
d,
param,
sigma,
model = c("log", "neglog", "bilog", "negbilog", "hr", "br", "xstud", "smith",
"schlather", "ct", "sdir", "dirmix", "pairbeta", "pairexp", "wdirbs", "wexpbs"),
weights = NULL,
vario = NULL,
coord = NULL,
grid = FALSE,
dist = NULL,
...
)
n 
number of observations 
d 
dimension of sample 
param 
parameter vector for the logistic, bilogistic, negative bilogistic and extremal Dirichlet (Coles and Tawn) model. Parameter matrix for the Dirichlet mixture. Degree of freedoms for extremal student model. See Details. 
sigma 
covariance matrix for BrownResnick and extremal Studentt distributions. Symmetric matrix of squared coefficients 
model 
for multivariate extreme value distributions, users can choose between 1parameter logistic and negative logistic, asymmetric logistic and negative logistic, bilogistic, HuslerReiss, extremal Dirichlet model (Coles and Tawn) or the Dirichlet mixture. Spatial models include the BrownResnick, Smith, Schlather and extremal Student maxstable processes. 
weights 
vector of length 
vario 
semivariogram function whose first argument must be distance. Used only if provided in conjunction with 
coord 

grid 
Logical. 
dist 
symmetric matrix of pairwise distances. Default to 
... 
additional arguments for the 
The vector param differs depending on the model
log
: one dimensional parameter greater than 1
neglog
: one dimensional positive parameter
bilog
: d
dimensional vector of parameters in [0,1]
negbilog
: d
dimensional vector of negative parameters
ct
, dir
, negdir
: d
dimensional vector of positive (a)symmetry parameters. Alternatively, a d+1
vector consisting of the d
Dirichlet parameters and the last entry is an index of regular variation in (0, 1]
treated as scale
xstud
: one dimensional parameter corresponding to degrees of freedom alpha
dirmix
: d
by m
dimensional matrix of positive (a)symmetry parameters
pairbeta, pairexp
: d(d1)/2+1
vector of parameters, containing the concentration parameter and the coefficients of the pairwise beta, in lexicographical order e.g., \beta_{1,2}, \beta_{1,3}, \ldots
wdirbs, wexpbs
: 2d
vector of d
concentration parameters followed by the d
Dirichlet parameters
an n
by d
exact sample from the corresponding multivariate extreme value model
This functionality can be useful to generate for example Pareto processes with marginal exceedances.
Leo Belzile
Dombry, Engelke and Oesting (2016). Exact simulation of maxstable processes, Biometrika, 103(2), 303–317.
Boldi (2009). A note on the representation of parametric models for multivariate extremes. Extremes 12, 211–218.
set.seed(1)
rmevspec(n=100, d=3, param=2.5, model='log')
rmevspec(n=100, d=3, param=2.5, model='neglog')
rmevspec(n=100, d=4, param=c(0.2,0.1,0.9,0.5), model='bilog')
rmevspec(n=100, d=2, param=c(0.8,1.2), model='ct') #Dirichlet model
rmevspec(n=100, d=2, param=c(0.8,1.2,0.5), model='sdir') #with additional scale parameter
#Variogram gamma(h) = scale*h^alpha
#NEW: Variogram must take distance as argument
vario < function(x, scale=0.5, alpha=0.8){ scale*x^alpha }
#grid specification
grid.coord < as.matrix(expand.grid(runif(4), runif(4)))
rmevspec(n=100, vario=vario,coord=grid.coord, model='br')
## Example with Dirichlet mixture
alpha.mat < cbind(c(2,1,1),c(1,2,1),c(1,1,2))
rmevspec(n=100, param=alpha.mat, weights=rep(1/3,3), model='dirmix')
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